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3 July, 11:06

A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

1] Find a function that models the total area of the four pens. (Let w be the width of the rectangular area and A (w) be the area.)

2]Find the largest possible total area of the four pens. (Round your answer to one decimal place.)

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  1. 3 July, 11:23
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    2 W + 5 L = 750 ft

    5 L = 750 - 2 W

    L = 150 - 2 W / 5

    A (W) = W * (150 - 2 W / 5)

    A function that models the total area:

    A (W) = 150 W - 2 W² / 5

    A' (W) = 150 - 4 W / 5

    150 - 4 W / 5 = 0

    4 W / 5 = 150

    W = 187.5 ft

    The largest possible area:

    A = 150 * 187.5 - (2 * 187.5²) / 5 = 28,125 - 14,062.5 = 14,062.5 ft²
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